Why are two mistakes not worse than one? A proposal for controlling the expected number of false claims.

Multiplicity is common in clinical studies and the current standard is to use the familywise error rate to ensure that the errors are kept at a prespecified level. In this paper, we will show that, in certain situations, familywise error rate control does not account for all errors made. To counteract this problem, we propose the use of the expected number of false claims (EFC). We will show that a (weighted) Bonferroni approach can be used to control the EFC, discuss how a study that uses the EFC can be powered for co-primary, exchangeable, and hierarchical endpoints, and show how the weight for the weighted Bonferroni test can be determined in this manner. ©2016 The Authors. Pharmaceutical Statistics Published by John Wiley & Sons Ltd.